1. Transport in a field aligned magnetized plasma and neutral gas boundary:
The end of the plasma…
C.M. Cooper, W. Gekelman, P. Pribyl, J. Maggs, Z. Lucky
University of California, Los Angeles
February 15, 2013

2. Overview Motivation Summary of Enormous Toroidal Plasma Device
Relation to Auroral Physics, Divertor Physics
Summary of Enormous Toroidal Plasma Device
Model of ETPD plasma regions
Neutral Boundary Layer model: Plasma Termination
Occurs at plasma/neutral gas pressure equilibrium
Plasma terminates on current-free ambipolar sheath determined by a generalized Ohm’s law
Heating, ionization occur in NBL
Measured scaling laws in ETPD

3. Motivation: Aurora J. Borovsky, J. Geo Res 98, A4 6101-6138 (1993)
The auroral-arc current loop associated with a perpendicular electric field imposed in the magnetosphere [Borovsky 1993]
Aurora over Jokulsarlon Lake, Iceland
Stephane Vetter, “Nuits sacrees” Feb. 2011
Schematic view of parallel currents j||, plasma motions, vperp, electric fields, and potential contours above auroral arc, sketched in green [Haerendel 1996]
J. Borovsky, J. Geo Res 98, A (1993)
G. Haerendel, J. Atmos. Terr. Phys. 58, (1996)

4. Motivation: Gaseous Divertors
Gaseous divertor design for DIII-D
Gaseous divertors designed to dissipate plasma particles, momentum, and energy on neutral gas before touching wall
Gaseous divertor design for JET
R. W. Conn, Fusion and Eng. Design (1991)

5. Diagram of the ETPD
Toroidal Magnets (red) provide a 250 G confining field
Vertical Magnets (blue) provide a 6 G vertical field to space out rings
LaB6 source injects primaries to form then heat the plasma
ETPD Plasma (pink) follows the helical magnetic field up to 120 m
C.M. Cooper et al, Rev of Sci Inst (2010)
R.J. Taylor et al, Nuclear Fusion (2002)

6. Picture of a LaB6 Cathode
Frame and Shielding
Heater
Anode
Cathode

7. Experimental Setup
Primary electrons boiled off LaB6 are accelerated along the field by anode.
Primaries ionize neutral gas to create and heat plasma.
Data taken where plasma ends, 90% around machine.

8. Neutral Boundary Layer
Probe
400 V discharge
2 mTorr
300 V discharge
2.5 mTorr
220 V discharge
3.6 mTorr
2.2 kA

9. Energy Balance in Aurora
Energy Balance in ETPD
220 V e
HEAT e
HEAT
Helium
Gas B
Ionosphere
HEAT e e i
HEAT
Atmo-
sphere
<100 kV
Energy Balance in Aurora

10. 3 Zones in ETPD Plasma Take Data Heat Density
+ Thermalization of primaries
+ ionization > losses
Conduction/ ionization
- Radial diffusion
Ohmic Heating and cooling
- Ionization and Radial diffusion
Heat
Density
Take Data
Energy input length
Energy loss length
Efield Term.

11. Ambipolar Termination Sheath in NBL!
Plasma potential in neutral gas boundary indicative of large field-aligned electric field 1 -1 -2 -3 -4 40 20
-20
-40
All plots generated from z2011_02_ep_plots, colorbar moveable, vplasma4 is on dif col
Relative y coord (cm)
Fp (eV)
Relative x coord (cm)
Relative x coord (cm)
Relative x coord (cm)
Relative x coord (cm)
Neutral fill of 3.6 mTorr He, a plasma discharge of 194 A 220 V, Btor=250 G, Bver=6 G,

12. Generate Radial Profiles
Used to study rate at which particles, momentum, and heat move across the field and out of the plasma 1 -1 -2 -3 -4 40 20
-20
-40
All plots generated from z2011_02_ep_plots, colorbar moveable, vplasma4 is on dif col
Relative y coord (cm)
Fp (eV)
Relative x coord (cm)
Relative x coord (cm)
Relative x coord (cm)
Relative x coord (cm)
Neutral fill of 3.6 mTorr He, a plasma discharge of 194 A 220 V, Btor=250 G, Bver=6 G,

13. Generate Axial Profiles in NBL
Plot data along the center of plasma coordinate “s”
Three zones!
A B C A B C 1 -1 -2 -3 -4 40 20
-20
-40
All plots generated from z2011_02_ep_plots, colorbar moveable, vplasma4 is on dif col
Relative y coord (cm)
Fp (eV)
Relative x coord (cm)
Relative x coord (cm)
Relative x coord (cm)
Relative x coord (cm)
Neutral fill of 3.6 mTorr He, a plasma discharge of 194 A 220 V, Btor=250 G, Bver=6 G,

14. Neutral Boundary Layer Model
Three-fluid, current-free
Continuity equation: ionization and losses A
Momentum equation: pressure equilibration
Momentum equation: generalized Ohms Law B
Heat equation: ionization and Ohmic heating C

15. Zone A: Pressure Equilibration
For
𝑝 𝑝 ≥ 𝑝 𝑛
Diffusivity argument: Neutral density convected out along field by plasma, diffuses across field
𝐷 𝑎,|| ≫ 𝐷 𝑛 = 𝑘 𝐵 𝑇 𝑛 𝜈 𝑛 > 𝐷 𝑎,⊥
Drag force limited to cross-field neutral diffusion rate
𝝂 𝒅𝒓𝒂𝒈 = 𝜵 ⊥ 𝜞 𝒏,⊥ / 𝒏 𝒏 ≤ 𝑫 𝒏 / 𝑹 𝒑 𝟐
Axial neutral flow develops from force balance
Momentum gained from plasma
𝑣 𝑛,𝑠 = 𝑣 𝑝,𝑠 𝟎.𝟓𝝂 𝒊𝒏 − 𝝂 𝒄𝒙 / 𝒏 𝒏 𝟎.𝟓𝝂 𝒊𝒏 − 𝝂 𝒄𝒙 / 𝒏 𝒏 + 𝜵 ⊥ 𝜞 𝒏,⊥ / 𝒏 𝒏
Momentum lost to stationary neutrals

16. Electron Temperature in Zone A-1 -2 -3
(eV) Fp
Constant
Ionization ~ 0 3 2
(eV) Te
Axial profiles generated from te_plots, ep_plots and bdot_plots Fits from 2011_02_getaxialprofiles, generated on 3/20/2012
Distance from anode (cm)

17. Plasma Velocity in Zone A-1 -2 -3
(eV) Fp
Plasma velocity is flat
Momentum balance
Sets a critical velocity 4 2
(105cm/s) vp
0.5
0.4
0.3
0.2
0.1
Plasma mach at 2.2 eV
Axial profiles generated from te_plots, ep_plots and bdot_plots Fits from 2011_02_getaxialprofiles, generated on 3/20/2012
Distance from anode (cm)

18. Plasma Density in Zone A-1 -2 -3
(eV) Fp
Plasma density is dropping from radial losses
1.2
0.8
0.4
(1012/cm3) ne
Axial profiles generated from te_plots, ep_plots and bdot_plots Fits from 2011_02_getaxialprofiles, generated on 3/20/2012
Distance from anode (cm)

19. Zone B: Ambipolar Electric Field
Current-free plasma sees neutral gas at end i e e i i e e
Electrons stop, ion current penetrates i i i e e i e i e e i
Electric field develops, drives electron current i i e e i i i e e e
Electric field maintains Current free term. i e i e i

20. Potential Structure in NBL
Plasma iso-potentials form “nested V’s”
White arrows show electric field, parallel field 10x
Quasineutral
lei
Axial profiles generated from te_plots, generated on 11/29/2011, used on all posters
Parallel arrows 10x
len lD
Colormap of plasma potential from 1,300 points interpolated onto toroidal coordinates

21. Electron Temperature in Zone B-1 -2 -3
(eV) Fp
Electron temperature rises with potential
For 3 2
(eV) Te Fp
Axial profiles generated from te_plots, ep_plots and bdot_plots Fits from 2011_02_getaxialprofiles, generated on 3/20/2012
Distance from anode (cm)

22. Plasma Velocity in Zone B-1 -2 -3
(eV) Fp
Plasma velocity drops due to drag on neutrals 4 2
(105cm/s) vp
0.5
0.4
0.3
0.2
0.1
Plasma mach at 2.2 eV
Axial profiles generated from te_plots, ep_plots and bdot_plots Fits from 2011_02_getaxialprofiles, generated on 3/20/2012
Distance from anode (cm)

23. The difference between momentum and temperature loss
Electrons
Momentum loss:
– faster
Energy loss:
– slower
In electric field, electrons HEAT.
Ions
Momentum loss:
– slower
Energy loss:
– faster
In electric field, ions SLOW.

24. Plasma Density in Zone B-1 -2 -3
(eV) Fp
Plasma density is dropping from radial losses
Balance between Flux conservation
Adiabatic heating
1.2
0.8
0.4
(1012/cm3) ne
Axial profiles generated from te_plots, ep_plots and bdot_plots Fits from 2011_02_getaxialprofiles, generated on 3/20/2012
Distance from anode (cm)

25. Plasma Termination
Use generalized Ohms law to solve for electric field

26. Zone C: Additional Ionization
R. K. Janev, Elementary Processes in Hydrogen and Helium Plasmas (1987)

27. Electron Temperature in Zone C-1 -2 -3
(eV) Fp
Prediction: Electron temperature continues to rise rapidly with potential 3 2
(eV) Te
Axial profiles generated from te_plots, ep_plots and bdot_plots Fits from 2011_02_getaxialprofiles, generated on 3/20/2012
Distance from anode (cm)

28. Electron Temperature in Zone C-1 -2 -3
(eV) Fp
IONIZATION 3 2
(eV) Te
Axial profiles generated from te_plots, ep_plots and bdot_plots Fits from 2011_02_getaxialprofiles, generated on 3/20/2012
Distance from anode (cm)

29. Plasma Density in Zone C-1 -2 -3
(eV) Fp
Prediction: Plasma density continues to drop
1.2
0.8
0.4
(1012/cm3) ne
Axial profiles generated from te_plots, ep_plots and bdot_plots Fits from 2011_02_getaxialprofiles, generated on 3/20/2012
Distance from anode (cm)

30. Plasma Density in Zone C-1 -2 -3
(eV) Fp
IONIZATION
1.2
0.8
0.4
(1012/cm3) ne
Axial profiles generated from te_plots, ep_plots and bdot_plots Fits from 2011_02_getaxialprofiles, generated on 3/20/2012
10%
Distance from anode (cm)

31. Plasma Production in Boundary
If all energy gained went into plasma production how much could you make? For
What’s the mean free path of ionization?
Any energy gained by electric field is quickly absorbed by ionization

32. Plasma Velocity in Zone C-1 -2 -3
(eV) Fp
Prediction: Plasma velocity will drop to 0 4 2
(105cm/s) vp
0.5
0.4
0.3
0.2
0.1
Plasma mach at 2.2 eV
Axial profiles generated from te_plots, ep_plots and bdot_plots Fits from 2011_02_getaxialprofiles, generated on 3/20/2012
Distance from anode (cm)

33. Plasma Velocity in Zone C-1 -2 -3
(eV) Fp
Additional flux is generated by the ionization at the end of the plasma
Still slowing down after ionization ends
IONIZATION 4 2
(105cm/s) vp
0.5
0.4
0.3
0.2
0.1
Plasma mach at 2.2 eV
Axial profiles generated from te_plots, ep_plots and bdot_plots Fits from 2011_02_getaxialprofiles, generated on 3/20/2012
Distance from anode (cm)

34. NBL Conserved Quatities
Normalized Plasma Pressure:
Axial Plasma Flux: 4 2
1.4
1.0
0.6
Gp,s=npvp,s
Pp=(np(Ti+Te)/(nnTn))
Distance from anode (cm)
Distance from anode (cm)
Axial profiles generated from te_plots, ep_plots and bdot_plots Fits from 2011_02_getaxialprofiles, generated on 3/20/2012
Normalized Plasma Pressure:
End of the plasma occurs where pp=pn
Dropping pressure “interrupted” by termination E field
Plasma flux:
Measure of axial particle flux
Only loss of axial flux is radial flux
Filling in of profile
Kinetic effects (trapped particles)

35. Scaling of Ambipolar Electric Field
The potential marks a “footprint” for the boundary of the plasma
49 kW
43 kW
39 kW
The location and magnitude of Electric field terminating the plasma change as a function of input power
Measure plasma
parameters

36. Scaled Plasma Parameters pre-NBL
Te is flat at 2.2 eV
(b)
Extra power raises density
Axial flow drops
(c)

37. Scaling Study pp=pn seq,m=seq,t Es,m=Es,t
Measured electric field, Es,m, scales like the theoretical ambipolar value
Measured termination point, seq,m, coincides with location of pressure equilibration

38. Modified Ambipolar Flow in ETPD
Electron current
Ion current
Electron current
Ion current
Ion current
Electron current

39. Ambipolar Flow in NBL
Magnetic field data from probe indicates axial current
Negative current carried by electrons moving in positive direction
Data taken at s = 2870 cm, halfway through NBL

40. Non-Zero Current in NBL
NBL not current free
Current trends to zero
Drift speed associated with current << bulk flow
Axial profiles generated from te_plots, triangles are current in boundary,
redlines is integrated pederson current /8
0.9 𝑣 𝑒,𝑠 < 𝑣 𝑖,𝑠 < 𝑣 𝑒,𝑠

41. Types of Current
Some currents diverge and need to be closed to maintain J=0
Note: Steady
state so Jpolz = 0
Divergence-Free
Non Divergence-Free
Some currents are associated with particle drifts and transport
Parallel (e-n) Current
Radial Pederson (i-n) Current
Vertical/B Currents
Poloidal Hall (i-n) Current (+)
Transport Causing
Poloidal Diamagnetic Current (-)
Non Transport Causing

42. Estimation of Jr Jr JS JSo+DS = JSo + Jr Ar AS
Axial current tied to Radial current JS Ar
JSo+DS = JSo Jr AS
Kirchoff’s Junction Rule

43. Future Work on NBL Observational Experimental Simulation
Measure plasma potential and flows in Aurora
Experimental
Study NBL for different pressures and/or gases
Simulation
Model in DEGAS (neutral gas collisional code)*
Model in UEDGE (transport code)*
Runge Kutta solver for fluid model**

44. Future work: 1.5-D Simulation
Measured 5 things: Model neutral gas Solve 5 equations + neutral gas transport:
Generalized Source/Sink
calibrated by data

45. Conclusions Plasma terminates on ambipolar electric field
Electric field occurs where diminishing plasma pressure and neutral pressure equilibrate
NBL dominated by termination field through Ohmic heating and ionization
NBL has a small modified ambipolar diffusion due to differences in directional particle motilities

46. Thanks!